Abstract
We construct a supersymmetric flipped SU(5) grand unified model that possesses an R symmetry. This R symmetry forbids dangerous non-renormalizable operators suppressed by a cut-off scale up to sufficiently large mass dimensions so that the SU(5)-breaking Higgs field develops a vacuum expectation value of the order of the unification scale along the F- and D-flat directions, with the help of the supersymmetry-breaking effect. The mass terms of the Higgs fields are also forbidden by the R symmetry, with which the doublet-triplet splitting problem is solved with the missing partner mechanism. The masses of right-handed neutrinos are generated by non-renormalizable operators, which then yield a light neutrino mass spectrum and mixing through the seesaw mechanism that are consistent with neutrino oscillation data. This model predicts one of the color-triplet Higgs multiplets to lie at an intermediate scale, and its mass is found to be constrained by proton decay experiments to be ≳ 5 × 1011 GeV. If it is ≲ 1012 GeV, future proton decay experiments at Hyper-Kamiokande can test our model in the p → π0μ+ and p → K0μ+ decay modes, in contrast to ordinary grand unified models where p → π0e+ or p → {K}^{+}overline{nu} is the dominant decay mode. This characteristic prediction for the proton decay branches enables us to distinguish our model from other scenarios.
Highlights
The 10 and 5 representations for the MSSM matter fields and 5 and 5 for the MSSM Higgs fields
We construct a supersymmetric flipped SU(5) grand unified model that possesses an R symmetry. This R symmetry forbids dangerous non-renormalizable operators suppressed by a cut-off scale up to sufficiently large mass dimensions so that the SU(5)breaking Higgs field develops a vacuum expectation value of the order of the unification scale along the F - and D-flat directions, with the help of the supersymmetry-breaking effect
The mass terms of the Higgs fields are forbidden by the R symmetry, with which the doublet-triplet splitting problem is solved with the missing partner mechanism
Summary
We study the vacuum structure of this model. In the following analysis, we assume the canonical form of the Kähler potential, K = |Fiαβ|2 + . . . , just for simplicity. We include the effect of non-renormalizable operators and soft SUSY breaking masses, with which the potential terms for the above fields are VF λH Λ5H S (νHc νHc ). To estimate the size of the VEVs of Φ and S with a simple analysis, we take λHS to be real and positive In this case, we can express the potential in terms of Φ ≡ |Φ|eiθ and S as. The same operators as in eq (2.6) with a slightly lower effective cut-off scale can be generated by additional fields around the Planck scale; for instance, suppose that there are two singlet chiral superfields, φ and φ, with U(1)R charges 19/18 and 17/18, respectively, which have the superpotential interactions.
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